Finite Group Databasebeta

← #35308572

Subgroups — #35308572

Order 21248.

326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918857C211yesmaximal, characteristic
2#24907603C211yesmaximal, characteristic
3#24906194C212yesmaximal
4#24906079C212yesmaximal
5C83×#1307C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127987—22no—
8#19127959—22no—
9#19127912—22no—
10#19127725C2211yescharacteristic
11C2×#14581703C2211yescharacteristic
12#19127465—22no—
13#19127449—22no—
14#19127446—22no—
15#19127442—24no—
16#432×C83C2212yes—
17#423×C83C2211yescharacteristic
18C2×Dic332—22no—
19C2×#13050574—21no—
20C22×C83⋊C8—21no—
21#14581792D412yes—
22#14581792D412yes—
23#14581784—22no—
24#14581771—22no—
25#14581771—22no—
26C4×Dic166—22no—
27C4×Dic166—22no—
28#14581751—22no—
29#14581724—22no—
30C4⋊(C83⋊C8)—22no—
31#14581717—24no—
32#14581703—21no—
33#14581703D412yes—
34C2×M16×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C22⋊C8×C83—22no—
39#97×C83—22no—
40C2×Dic166—22no—
41C2×Dic166—22no—
42Dic332—82no—
43#13050574—42no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8—41no—
46C2×C83⋊C8—41no—
47C2×C83⋊C8—41no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52Dic83⋊C4—42no—
53Dic83⋊C4—42no—
54C22⋊Dic83—42no—
55C4×Dic83—42no—
56C22×C4×C83C2×D411yescharacteristic
57C22×C4×C83#4112yes—
58M16×C83—42no—
59C2×C8×C83—22no—
60C2×C8×C83—42no—
61C42×C83C2×D412yes—
62C42×C83C2×D411yescharacteristic
63C42×C83#4111yescharacteristic
64C23×C83#12411yescharacteristic
65C2×C4×C83—21no—
66C2×C4×C83—21no—
67C2×C4×C83—42no—
68C2×C4×C83#12011yescharacteristic
69C2×C4×C83#12112yes—
70C2×C4×C83#12111yescharacteristic
71C2×C4×C83#12312yes—
72C2×Dic83—42no—
73C2×Dic83—42no—
74Dic166—42no—
75Dic166—42no—
76Dic166—82no—
77C8×C83—42no—
78C8×C83—82no—
79C83⋊C8—42no—
80C83⋊C8—81no—
81C22×C83—22no—
82C22×C83—21no—
83C22×C83#39411yescharacteristic
84C4×C83—22no—
85C4×C83—22no—
86C4×C83—21no—
87C4×C83#45411yescharacteristic
88C4×C83#45511yescharacteristic
89Dic83—82no—
90Dic83—82no—
91#10529—831nomaximal, Sylow
92C2×C83—41no—
93C2×C83#204011yescharacteristic
94C2×C83#204912yes—
95#3255—831no—
96#1838—831no—
97#1559—832no—
98#1531—832no—
99#1307D8311yescharacteristic
100C83#1052911yescharacteristic, complemented, Sylow
101#533—832no—
102#475—1662no—
103#470—1662no—
104#462—1662no—
105#432C2×D8312yes—
106#423—831no—
107#423C2×D8311yescharacteristic
108C2×#97—831no—
109#341—1662no—
110#333—1662no—
111#332—1662no—
112#330—1664no—
113C2×Q16—1662no—
114C2×M16—1661no—
115C2×M16D33212yes—
116C22×C8—1661no—
117C4⋊Q8—832no—
118C4⋊Q8—832no—
119#125—1662no—
120C22⋊Q8—1662no—
121C22⋊Q8—1662no—
122C4×Q8—1662no—
123C4×Q8—1662no—
124#117—1662no—
125C2×C42C22×D8311yescharacteristic
126#106—1662no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—1662no—
130#103—1664no—
131C22⋊C8—22no—
132#97—22no—
133#97—832no—
134#97—1661no—
135C2×Q8—1662no—
136C2×Q8—1662no—
137C22×C4C2×D33211yescharacteristic
138C22×C4#1305059012yes—
139Q16—6642no—
140M16—42no—
141M16—3322no—
142C2×C8—22no—
143C2×C8—42no—
144C2×C8—3321no—
145C2×C8—3321no—
146C2×C8—3321no—
147C2×C8—1662no—
148C4⋊C4—3322no—
149C4⋊C4—3322no—
150C4⋊C4—1662no—
151C4⋊C4—1662no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C22⋊C4—3322no—
155C42—3322no—
156C42D4×D8312yes—
157C42D4×D8311yescharacteristic
158C42#1305059111yescharacteristic
159C23#1458178011yescharacteristic
160Q8—3322no—
161Q8—3322no—
162Q8—6642no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—3322no—
167C2×C4—3322no—
168C2×C4#1458176211yescharacteristic
169C2×C4#1458176512yes—
170C2×C4#1458176711yescharacteristic
171C2×C4#1458177712yes—
172C8—42no—
173C8—82no—
174C8—3322no—
175C8—6641no—
176C22—21no—
177C22—22no—
178C22#1912761911yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—6642no—
183C4—6642no—
184C4#1912787611yescharacteristic
185C4#1912788111yescharacteristic
186C2—41no—
187C2#2490869311yescharacteristic
188C2#2490874612yes—
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1307C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#1307D83
hypocenterC83#10529
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
100. C83#10529semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249188572
#249076032
#249061942
#249060792
C83×#13072
#1052983